The Review of Symbolic Logic

Research Article

A CUT-FREE SIMPLE SEQUENT CALCULUS FOR MODAL LOGIC S5

FRANCESCA POGGIOLESIa1 c1

a1 University of Florence and University of Paris 1

Abstract

In this paper, we present a simple sequent calculus for the modal propositional logic S5. We prove that this sequent calculus is theoremwise equivalent to the Hilbert-style system S5, that it is contraction-free and cut-free, and finally that it is decidable. All results are proved in a purely syntactic way.

(Received July 04 2007)

(Revised January 18 2008)

Correspondence:

c1 DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF FLORENCE, 50139 FLORENCE, ITALY. E-mail: francesca.poggiolesi@unifi.it